data collected by the chain are summarized in the table below. The data were obtained from a random sample of 190 people. The birthdate of each person was recorded,
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain in the Northwest asked just this question. Some data collected by the chain are summarized in the table below.
The data were obtained from a random sample of 190 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories.
Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the
level of significance for the test.
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Winter Spring Summer
Fall
Total
Observed
frequency
45
39
50
56
190
fo
Expected
frequency
47.50
47.50
47.50
47.50
fE
(fo fa
fE
0.132
1.521]
0.132
1.521](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dca6abf-c7a8-4de6-9769-4f15b1721207%2Fcc11ec76-8c51-408a-bd4e-b8d50a58ef76%2Fjr71n0e_processed.png&w=3840&q=75)
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